Geodesic
A Necessary Condition for the Completeness of the System $\{e^{-\lambda_nt}\mid\operatorname{Re}\lambda_n>0\}$ in the Spaces~$C_0(\mathbb R_+)$ and $L^p(\mathbb R_+)$, $p>2$
Matematičeskie zametki, Tome 83 (2008) no. 6, pp. 831-842.

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We obtain a necessary condition for the completeness of the system $$ e(\Lambda)=\{e^{-\lambda_nt}\mid\operatorname{Re}\lambda_n>0,\,n\in\mathbb Z\} $$ in the spaces $C_0$ and $L^p(\mathbb R_+)$, $p>2$, for the case in which the set of limit points of the sequence $\{\lambda_n\}$ is countable and separable.
Keywords: sequence of exponentials, the spaces $C_0(\mathbb R_+)$ and $L^p(\mathbb R_+)$, $p>2$, Hardy class of functions, Bernstein's inequality, analytic function.
Mots-clés : Szász condition 
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I. O. Krasnobaev. A Necessary Condition for the Completeness of the System $\{e^{-\lambda_nt}\mid\operatorname{Re}\lambda_n>0\}$ in the Spaces~$C_0(\mathbb R_+)$ and $L^p(\mathbb R_+)$, $p>2$. Matematičeskie zametki, Tome 83 (2008) no. 6, pp. 831-842. http://geodesic.mathdoc.fr/item/MZM_2008_83_6_a3/

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